How can I get more saturated colors when I render?
Watch your albedos. It doesn't matter if you use pure primaries or highly saturated colours; Filmic will desaturate as things get too intense. High albedo will race those values through the roof quickly, leading to desaturation. As Cegaton wisely said, the old adages are pure rubbish based on a lack of understanding regarding view transforms; feel free to use as heavily saturated colours as you want when designing your looks for textures.
You can't have an object that is highly saturated and highly intense. It is simply impossible. Colour is a byproduct of the ratios of the three lights, which means that as the intensity increases, the room for those ratios become more and more limited. Find the sweet spot keeping your colour within the exposure range.
There is an intimate relationship between the apparent saturation and the contrast. Try to be delicate with contrast adjustments that focus on the saturation you desire. For a fulcrum based contrast tweak around middle grey, divide your render by 0.18, use the power function of the CDL, then multiply by 0.18 on the other side. This will adjust contrast based around the middle grey point as a fulcrum.